Factor -12x^2-35x-18

$- 12 x^{2} - 35 x - 18$

Step 1

Factor $- 1$ out of $- 12 x^{2} - 35 x - 18$ .

Factor $- 1$ out of $- 12 x^{2}$ .

$- (12 x^{2}) - 35 x - 18$

Factor $- 1$ out of $- 35 x$ .

$- (12 x^{2}) - (35 x) - 18$

Rewrite $- 18$ as $- 1 (18)$ .

$- (12 x^{2}) - (35 x) - 1 (18)$

Factor $- 1$ out of $- (12 x^{2}) - (35 x)$ .

$- (12 x^{2} + 35 x) - 1 (18)$

Factor $- 1$ out of $- (12 x^{2} + 35 x) - 1 (18)$ .

$- (12 x^{2} + 35 x + 18)$

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 12 \cdot 18 = 216$ and whose sum is $b = 35$ .

Factor $35$ out of $35 x$ .

$- (12 x^{2} + 35 (x) + 18)$

Rewrite $35$ as $8$ plus $27$

$- (12 x^{2} + (8 + 27) x + 18)$

Apply the distributive property.

$- (12 x^{2} + 8 x + 27 x + 18)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$- ((12 x^{2} + 8 x) + 27 x + 18)$

Factor out the greatest common factor (GCF) from each group.

$- (4 x (3 x + 2) + 9 (3 x + 2))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2$ .

$- ((3 x + 2) (4 x + 9))$

Remove unnecessary parentheses.

$- (3 x + 2) (4 x + 9)$

Factor -12x^2-35x-18

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